The Murry Bergtraum High School for Business Careers is next door to 1 Police Plaza and just a block away from City Hall.Helayne Seidman

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It was on YouTube for only a few hours, but in that time, to the mortification of city officials, it went global: the sight and sound of at least 100 students at Murry Bergtraum High School, located just next door to NYPD headquarters, rioting in the corridors, wrestling with officers who patrol the campus and one student punching a police sergeant in the face.

“The school doesn’t get why that would be a problem,” says one teacher at Murry Bergtraum.

That, she says, is how it’s written up in the paperwork. Six students were issued summonses for disorderly conduct, and a seventh was arrested for “obstructing governmental administrations.”

No one was arrested for assaulting an officer?

“No,” Crispin says. “They couldn’t tell who did it.”

No one was injured, Crispin says, and the school is usually only patrolled by unarmed school-safety agents — that police sergeant just happened to be there on “unrelated business.”

Large, disorderly groups; an armed cop who wasn’t called in a panic but just decided to swing by the most violent school in the city; a ranking sergeant who was clocked in the face yet unhurt — these are but a few of the euphemisms employed when officials are forced to address the educational and institutional disaster that is Murry Bergtraum High School — or, as it is known in city parlance, an “impact school.”

The irony of that Orwellian description — the most impact the school seems to have is best measured in body blows, punches and general emotional trauma among students and teachers — is clearly lost on those who would be in charge.

And that the story broke via cellphone video is yet another example of the disconnect between students and officials, who view them as weapons — kids have used them to organize riots — while students, who are supposed to turn over their phones at the start of every school day, view them as lifelines.

And why shouldn’t they? Thanks to a cellphone video, the world can see just how appalling and unsafe the conditions are at Murry Bergtraum High — conditions that the principal, the cops and the city would prefer to deny. Behind euphemisms and statistics, pictures are the only proof.

‘Over the past several years, I’ve seen many a teacher say, ‘I’m done, I’m out of here,’ ” says a Bergtraum teacher, who spoke only on the condition of anonymity. “It’s to the point where there aren’t any consequences for these kids. Since last week’s riot, there’s got to be 10 cops in this building every day. But I don’t know who can lay down the law here or who can enforce it.”

The riot broke out on the school’s second floor last Thursday morning around 11:30. No one knows why, although two 15-year-old boys beat up another student on campus the day before. Several students who spoke with The Post say that fights occur nearly once a day, with riots erupting once a month.

Bergtraum High last made news in December 2010, when students rioted after Principal Andrea Lewis, then fairly new, got on the loudspeaker and announced that bathroom breaks were banned for the day — an ill-advised response to yet another fight, which resulted in one student going to the ER.

The school promptly installed metal detectors, which spurred half the student body to stay home in protest. Among the kids who did show up, one threw a garbage can at a school-safety officer, sending him to the hospital. That same day, a 17-year-old was sent to Bellevue after getting punched in the head by a fellow student.

“It’s hell,” one 15-year-old sophomore says. “Most of the kids are really wild for no reason, and the teachers don’t know how to control them.”

Students who spoke with The Post say they are so accustomed to violence that when they hear the rumblings of a stampede, see teachers leap out of their chair to lock classroom doors and hear the screams of fellow students echo through the hallways, they don’t assume, the tragic way most other students around the country now do, that there’s a shooter on campus. These kids know it’s a riot over nothing, that no one can stop it and, at some point, it will end.

This time, it took cops and security guards 20 minutes to get the melee under control — and this is a school that can’t be reached without passing through three checkpoints, all patrolled by a uniformed police officer.

Bergtraum High was one of the first schools to be evacuated on Sept. 11, with nearly 2,000 students out of the building in three minutes. Today, in a part of the city that, by necessity and design, is inundated with cops, first responders, high-tech surveillance and all manner of experts in suspicious activity and crowd control, Bergtraum High operates as a lawless city-state unto itself. In an attempt to at least engender a cosmetic sense of order, Principal Lewis instituted school uniforms in the fall of 2011. Students choose not to wear them.

The Murry Bergtraum High School for Business Careers is named after one of the city’s former Board of Education presidents and, as recently as 1999, was ranked one of the best high schools in the nation. It was the first in the state to offer computer programming. Damon Wayans and John Leguizamo are among the alumni, as is New York state Assemblywoman Vanessa Gibson.

Today, it’s the most overcrowded school in New York City and, by most accounts, the worst. It’s an unintended byproduct of Mayor Bloomberg’s attempt at reform; since taking over the schools in 2002, the mayor has closed over 90 failing schools, and though 335 smaller, specialized ones have opened, there are a surplus of students that need to be placed somewhere.

“We’re getting the runoff of the schools systematically closed under Bloomberg,” says the Bergtraum teacher. “All of those undesirables get pushed off here.”

Overcrowding is perhaps the only identifiable factor in Bergtraum’s decline. Once one of the most elite high schools in the city — on par with Bronx Science or Stuyvesant — it was a place students competed to get into. These days, it’s a place you fall into. Schools can suffer vicious spirals — as fewer good students want to enroll, negative incidents increase, which only keeps more good students away. Little slips, year after year, add up to failure.

As of August 2011, student enrollment was at 2,562, with only 287 students taking the SAT, 118 taking AP exams and 48% of those passing. Just 18% are college-ready, and 12% drop out. On its last progress report, the city ranked the school a D, though an internal vote taken among 72 of Bergtraum’s teachers this past January resulted in an F.

Consider the official report of “violent and disruptive incidents” at Murry Bergtraum High from 2009-10, the last school year for which such data is available: one forcible-sex offense; seven assaults; 45 “intimidations”; five larcenies, 11 reports of criminal mischief, eight weapons possessions, eight alcohol possessions and two drug possessions.

No riots were reported, yet this was the same year of the “bathroom-break ban” incident, which was reported by every major media outlet and led to the installation of metal detectors and a guard getting assaulted by a student.

There were, however, 189 “other” incidents recorded.

Euphemisms.

In the micro, Bergtraum High is a sad, staggering symbol of the frustration of education reform in the US and an example that the city’s approach — closing failing schools, opening new ones, shunting troubled students into the few large schools left — is just slightly more sophisticated than whack-a-mole.

What’s most troubling is the utter lack of parental outrage at Murry Bergtraum High; students say that there’s been no blowback at all, no demands for answers or threats of lawsuits. Those who spoke with The Post offered several dispiriting explanations: Their parents were “too old” to use the Internet, too busy or simply, in the words of one, “don’t care.”

That leaves administrators and officials, who are paid to care. The Post called everyone — the principal, the United Federation of Teachers, the mayor’s office — and none would comment. The Department of Education also refused to go on record but maintains that it has been actively monitoring school safety and that conditions at the school are actually improving.

The explicit and implict denials that anything is really wrong at Murry Bergtraum are doubly offensive when juxtaposed with the raw video that leaked last week. Add to that the clear, unified strategy of refusing to comment, and its clear that, among officials, the fervent hope is the story dies, starved of oxygen.

Schools Chancellor Dennis Walcott was the only one to offer a brief statement to The Post.

“The incidents at Murry Bergtraum High School are troubling,” he said, “and we have redoubled our efforts at the school to prevent this from happening again.”